Can anyone tell me the value of the sum $$\sum_{p\in \mathcal{P}}\sum_{n=1}^{\infty}\frac{\log (p^n)}{2}\left[\,p^{-n}-\psi\left(\frac{p^n+2}{2}\right)+\psi\left(\frac{p^n+1}{2}\right)\right].$$ $\psi(z)$ is the digamma function. The sum is over primes using Mathematica.
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It is a related question I could not find the value of this sum – Surya Oct 14 '13 at 12:55
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1Read the answers to the linked question to get an idea how you could approximate the value. – Artes Oct 14 '13 at 12:58
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2Would you please post the code you used to try to find the sum? – Michael E2 Oct 14 '13 at 21:40